JEE Main 2016 Mathematics question

An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is

(1)
(2)
(3)
(4)Correct

Answer: (4)

Solution

"Succeeds twice as often as it fails" means , and with this gives and . The trials are independent, so the number of successes in trials is binomial. "At least 5 successes" means exactly 5 or exactly 6:

P = {}^

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Question ID VK-115673